| 作者简介 | 第1-8页 |
| 摘要 | 第8-14页 |
| Abstract | 第14-16页 |
| 1 Introduction | 第16-27页 |
| ·Aims and contribution of this thesis | 第17-19页 |
| ·Literature Review | 第19-25页 |
| ·Review of stability of Galerkin Methods for Reduced Order Mod-eling of the Navier-Stokes Equations | 第19-20页 |
| ·Review of non-linear reduction for Navier-stokes Equations | 第20-23页 |
| ·Review of reduced order 4D-var | 第23-25页 |
| ·Contents and ideas of the research | 第25页 |
| ·synopsis of thesis | 第25-27页 |
| 2 Numerical simulation of Navier-Stokes equations based on POD | 第27-43页 |
| ·Finite element discretisation method | 第27-33页 |
| ·Finite element discretisation of the Navier-Stokes Equations | 第33-34页 |
| ·Proper Orthogonal Decomposition | 第34-36页 |
| ·Reduced Order Modeling of Navier-stokes Equations using POD for un-structured adaptive mesh model | 第36-43页 |
| 3 A Petroy-Galerkin Reduced-order Modeling of the Navier-Stokes Equations using a mixed formulation | 第43-69页 |
| ·Governing Equations | 第44-45页 |
| ·A Scalar Petrov-Galerkin Transport Equation | 第45-50页 |
| ·Simplified scalar equation | 第48-49页 |
| ·Optimal Petrov-Galerkin methods | 第49-50页 |
| ·Nonlinear Time Dependent Equations | 第50-54页 |
| ·The Petrov-Galerkin Navier-Stokes equations | 第50-53页 |
| ·The simplified Petroy-Galerkin Navier-Stokes equations | 第53-54页 |
| ·Petrov-Galerkin Reduced Order Modelling | 第54-57页 |
| ·Application cases and numerical results | 第57-68页 |
| ·Case 1:flow past a cylinder | 第61-63页 |
| ·Case 2:Gyre | 第63-68页 |
| ·Summary and conclusions | 第68-69页 |
| 4 Non-Linear model reduction for the Navier-Stokes Equations using the residual DEIM method | 第69-97页 |
| ·Governing Equations | 第70-73页 |
| ·POD method for the Navier_Stokes Equations | 第73-79页 |
| ·The POD Model | 第74-77页 |
| ·Forming the POD formulation of the Navier Stokes' Equations | 第77-78页 |
| ·Stabilisation of the POD Model | 第78-79页 |
| ·Efficient treatments of the Non-linear operators | 第79-86页 |
| ·DEIM treatment of the Non-Linear Operator | 第80-83页 |
| ·Quadratic expansion of the Non-Linear Operator | 第83-84页 |
| ·The Residual DEIM Method | 第84-86页 |
| ·Numerical Examples | 第86-91页 |
| ·Case 1:Flow past a cylinder | 第87-88页 |
| ·Case 2:The Gyre problem | 第88-91页 |
| ·Conclusions | 第91-97页 |
| 5 Reduced order 4D Var data assimilation based on POD/DEIM | 第97-109页 |
| ·POD/DEIM Reduced Order Modelling | 第98-102页 |
| ·Proper Orthogonal Decomposition | 第98-99页 |
| ·POD reduced order modelling | 第99-100页 |
| ·Acceleration of the POD reduced model | 第100-102页 |
| ·4D Var based on POD/DEIM | 第102-106页 |
| ·Discrete reduced order adjoint equaions | 第103-106页 |
| ·Numerical Examples | 第106-107页 |
| ·conclusion | 第107-109页 |
| 6 Summary and future work | 第109-112页 |
| Acknowledgements | 第112-113页 |
| Bibliography | 第113-126页 |
